Heat the oven to 350 degrees, and spray two loaf pans well with baking spray.
Blend together the eggs, sugar, lemon zest, and lemon juice until well combined.
Add in the butter and vanilla.
Mix in the flour, baking powder, salt, and baking soda until just combined. Be careful not to overmix the batter.
Spread the mixture between the two loaf pans.
Bake for 25 minutes, then lower the heat to 325 and bake for another 30 minutes, or until cooked through.
Place the ingredients for the syrup into a saucepan over medium heat. Simmer until the sugar has melted.
Once the loaves have cooled slightly, poke holes in the tops and sides, then brush the syrup onto the loaves.
Mix together the ingredients for the glaze, and pour it over the top of the loaves.
Let the loaves cool and serve.